And I'll agree when you are right. Correct, Power = current x voltage (DC or instantaneous if AC).
Incorrect. Current is the only rating that matters for a wire. The power dissipated in the wire is (current)^2 * (resistance). This power must be dissipated as heat and conducted away. The later is different between home installation and appliances, so different current ratings. The voltage rating of the wire is for when the electrical insulation breaks down (arcs to ground).